The construction of space curves with rational rotationminimizing frames (RRMF curves) by the interpolation of G1 Hermite data, i.e., initial/final points pi and pf and frames (ti,ui,vi) and (tf ,uf ,vf ), is addressed. Noting that the RRMF quintics form a proper subset of the spatial Pythagorean–hodograph (PH) quintics, characterized by a vector constraint on their quaternion coefficients, and...

Let $X/\mathbb {F}_{q}$ be a smooth, geometrically connected, quasi-projective scheme. $\mathcal {E}$ semi-simple overconvergent $F$ -isocrystal on $X$ . Suppose that irreducible summands {E}_i$ of have rank 2, determinant $\bar {\mathbb {Q}}_p(-1)$ , and infinite monodromy at $\infty$ further for each closed point $x$ the characteristic polynomial is in $\mathbb {Q}[t]\subset \mathbb {Q}_p[t]$...

In this paper we present an application of the propositional SATisfiability environment to computing some simple orthogonal matrices and some interesting tasks in the area of cryptanalysis. We show how one can code a search for some kind of desired objects as a propositional formulae in such a way that their satisfying valuations code such objects. Some encouraging (and not very encouraging) ex...

Let f 2 Fq [x] be a monic polynomial of degree n, and let (f) denote the number of polynomials in Fq [x] of degree < n that are relatively prime to f . Let (f) = (f)=qn. We slightly improve the previous known lower bounds of (f). The density of normal elements in Fqn over Fq is (xn 1) = (xn 1)=qn. We prove that (xn 1) C > 0 for n = pe1 1 pe2 2 pet t where pi are any xed primes, ei vary, and C i...

This report considers a discrete fractional quadratic optimization problem motivated by a recent application in blind maximum-likelihood (ML) detection of higher-order QAM orthogonal spacetime block codes (OSTBCs) in wireless multiple-input multiple-output (MIMO) communications. Since this discrete fractional quadratic optimization problem is NP-hard in general, we present a suboptimal approach...

The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of graphs P1, . . . ,Pk (usually describing some common graph properties), is to decide, for a given graph G, whether the vertex set of G can be partitioned into sets V1, . . . , Vk such that, for each i, the induced subgraph of G on Vi belongs to Pi. It can be seen that GCOL generalizes many natural colouri...

This talk reports on an analytic derivation of the complete stability region of the Proportional Integral (PI) Active Queue Management (AQM). The stability region represents the entire set of the feasible design parameters, i.e., the proportional and the integral gains, that stabilize the closed-loop TCP-AQM system. AQM controls congestion by proactively marking or dropping packets before the i...

We develop a polynomial translation from finite control π-calculus processes to safe low-level Petri nets. To our knowledge, this is the first such translation. It is natural in that there is a close correspondence between the control flows, enjoys a bisimulation result, and is suitable for practical model checking.

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.